Did you know that no matter how fast a train is moving forward, there is always a part of the train that is moving backwards? Remember, a train runs on a flanged wheel riding on the train track. The flange has a larger diameter that the part of the wheel in contact with the track. The flange is represented by the point outside the yellow gear, illustrated above. Granted, the part of the train moving backwards is small and only moves backwards for an instant before it starts to move forward again. There is always a small part of the flange that loops from going forward to backwards to forward again. Notice the tracing of the point outside the circumference of the gear as the gear rolls along the rack.

Even though I stand by my reasons for drawing this curve in an upside down orientation, I realize the explanation of the flanged wheel effect would be easier to understand if the curve were in the normal position. I plan to add a graphic to this page in the near future helping to illustrate this amazing fact.